Test 3 Section 3 #20

To get this one, first draw triangle ABC with the information given: angle *B* is a right angle,

*BC* = 16, and *AC* = 20.

Because you know your Pythagorean triples, you know that this is a big cousin of the 3-4-5 triangle—it’s a 12-16-20!

Now, let me point out something that you may already have realized: if triangle *DEF* is similar to triangle *ABC*, that means it has the same angles! Since the sine of an angle is always the same ratio regardless of the lengths of the sides in any particular triangle, **we don’t need to draw DEF or calculate its side lengths to know what the sine of angle F is!** The question tells us that angle

*F*corresponds to angle

*C*, so sin

*F*= sin

*C*. All we need to do is calculate the sine of C. So, SOH-CAH-TOA that bad boy.

Note that you can grid the fraction, 3/5, or the decimal equivalent .6 and be correct.